Versatile focal field design using cascaded artificial neural network

Both forward and inverse design methods have been developed for focal field engineering, which has applications in many areas including super-resolution imaging and optical lithography, high-density optical storage, and particle manipulation. However, a certain method is normally targeted at a unique focal field distribution. Here, we report on a versatile focal field design method based on a cascaded artificial neural network (CANN) for the inverse design of focal field distributions in a high numerical aperture focusing system. The CANN consists of a forward and an inverse artificial neural network. Once trained properly, the CANN can predict modulation phase patterns for multiple focal field distributions. We demonstrate the effectiveness of the CANN by the design of focal field distributions along the optical axis including a uniform optical needle and an anti-point spread function with lengths up to 14 wavelengths and multiple focal spots with controllable intensities as well as those in the focal plane including flat-top and sub-diffraction focal spots.